Vessel Peclet number

Multiplying this number with the term ZJd, where Z is the fixed-bed length, we obtain the vessel Peclet number. A high vessel Peclet number means better flow quality, thus closer to ideal flow. Typically, if this number is higher than about 100, the flow is considered to be ideal (plug flow). 

Dispersion Model An impulse input to a stream flowing through a vessel may spread axially because of a combination of molecular diffusion and eddy currents that together are called dispersion. Mathematically, the process can be represented by Fick s equation with a dispersion coefficient replacing the diffusion coefficient. The dispersion coefficient is associated with a linear dimension L and a linear velocity in the Peclet number, Pe = uL/D. In plug flow, = 0 and Pe oq and in a CSTR, oa and Pe = 0. 

Both phases are siibstantiaUy in plug flow. Dispersion measurements of the hquid phase usuaUy report Peclet numbers, Uid /D, less than 0.2. With the usual smaU particles, the waU effect is negligible in commercial vessels of a meter or so in diameter, but may be appreciable in lab units of 50 mm (1.97 in) diameter. Laboratory and commercial units usuaUy are operated at the same space velocity, LHSy but for practical reasons the lengths of lab units may be only 0.1 those of commercial units. 

PeL Peclet number based on vessel length, uLIDi... 

The ratio, L/D, of length to diameter of a packed tube or vessel has been found to affect the coefficient of heat transfer. This is a dispersion phenomenon in which the Peclet number, uL/Ddisp, is involved, where D Sp is the dispersion coefficient. Some 5000 data points were examined by Schliinder (1978) from this point of view although the effect of L/D is quite pronounced, no dear pattern was deduced. Industrial reactors have LID above 50 or so Eqs. (6) and (7) of Table 17.18 are asymptotic values of the heat transfer coefficient for such situations. They are plotted in Figure 17.36(b). 

The dimensionless term (9/u0 L, where 9 is the axial dispersion coefficient, u0 is the superficial fluid velocity, and L is the expanded-bed height) is the column-vessel dispersion number, Tc, and is the inverse of the Peclet number of the system. Two limiting cases can be identified from the axial dispersion model. First, when 9/u0L - 0, no axial dispersion occurs, while when 9/u0 L - 00 an infinite diffusivity is obtained and a stirred tank performance is achieved. The dimensionless term Fc, can thus be utilized as an important indicator of the flow characteristics within a fluidized-bed system.446... 

To facilitate a semi-quantitative comparison of mass transfer in traditional in vitro culture vessels and perfusion based microfluidic cell culture chips, the Peclet number (Eq. 1) has been used [4] ... 

The reaction rate parameters are usually known (i.e., Da), but the Peclet number is usually not known because it depends on the flow and the vessel. Consequently, we need to find Pe using one of the three techniques discussed earlier in the chapter. 

Interstitial flows were measured by observing the motion of a spot bleached into fluorescent interstitial fluid in a tissue window preparation [10]. In this system, the fluid velocity was 0.2/ m/s parallel to the vessel and 0.75/xm/s perpendicular to the vessel. Convection was heterogeneous throughout the tissue region, but over a relatively small range (0.1 < u < 1 /xm/s). This rate of interstitial flow corresponds to a Peclet number (Pe) for BSA and IgG of 1, suggesting that convection and diffusion are equally important in the movement of macromolecules in the interstitial space. 

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